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This work deals with the numerical localization of small electromagnetic inhomogeneities.The underlying inverse problem considers,in a three-dimensional bounded domain,the time-harmonic Maxwell equations formulated in electric field.Typically,thedomain contains a finite number of unknown inhomogeneities of small volume and theinverse problem attempts to localize these inhomogeneities from a finite number of boundarymeasurements.Our localization approach is based on a recent framework that uses anasymptotic expansion for the perturbations in the tangential boundary trace of the curlof the electric field.We present three numerical localization procedures resulting from thecombination of this asymptotic expansion with each of the following inversion algorithms:the Current Projection method,the MUltiple SIgnal Classification (MUSIC) algorithm,and an Inverse Fourier method.We perform a numerical study of the asymptotic expansionand compare the numerical results obtained from the three localization procedures indifferent settings.
This work deals with the numerical localization of small electromagnetic inhomogeneities. The underlying inverse problem considers, in a three-dimensional bounded domain, the time-harmonic Maxwell equations formulated in electric field.Typically, the domain contains a finite number of unknown inhomogeneities of small volume and theinverse problem attempts to localize these inhomogeneities from a finite number of boundarymeasurements.Our localization approach is based on a recent framework that uses anasymptotic expansion for the perturbations in the tangential boundary trace of the curl of the electric field. We present three numerical local procedures from the combination of this asymptotic expansion with each of the following inversion algorithms: the Current Projection method, the MUltiple SIgnal Classification (MUSIC) algorithm, and an Inverse Fourier method. We perform a numerical study of the asymptotic expansion and compare the numerical results obtained from the three local ization procedures indifferent settings.